Applications of Derivatives Test

Result

Applications of Derivatives Test - 10

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Weekly Quiz Competition

Question 1
4 / -1

The length of the subtangent at any point (x₁, y₁) on the curve y = a^x (a > 0) is

A
2 log a

B
1/log a

C
log a

D

Solution
Question 2
4 / -1

The absolute maximum of x⁴⁰ - x²⁰ on the interval [0, 1] is

A
-1/4

B
0

C
1/4

D
1/2

Solution
Question 3
4 / -1

The point on the curve √x + √y = √a, the normal at which is parallel to the X - axis is

A
(0, 0)

B
(0, a)

C
(a, 0)

D
(a, a)

Solution
Question 4
4 / -1

If f(x) = 1 + 2x² + 2² x⁴ + ...+2¹⁰ x²⁰. Then, f(x) has

A
more than one minimum

B
exactly one minimum

C
at least one maximum

D
None of the above

Solution
Question 5
4 / -1

A
-1, 1

B
-2, 2

C
-3, 3

D
-4, 4

Solution
Question 6
4 / -1

The equation of the tangent to the curve x = 2 cos³ θ and y = sin³θ at the point, θ = π/4 is

A
2x + 3y = 3√2

B
2x - 3y = 3√2

C
3x + 2y = 3√2

D
3x + 2y = 3√2

Solution
Question 7
4 / -1

The minimum value of 4e^2x + 9e^-2x is

A
11

B
12

C
10

D
14

Solution
Question 8
4 / -1

Let f '(x) be differentiable for all x. If f(1) = - 2 and f '(x) ≥ 2, ∀ x ϵ [1, 6], then

A
f(6) < 8

B
f(6) ≥ 8

C
f(6) ≥ 5

D
f(6) ≤ 5

Solution
Question 9
4 / -1

The value of c from the Lagrange's mean value theorem for which

A
5

B
1

C
√15

D
None of these

Solution
Question 10
4 / -1

What are the value of c for while Rolle's theorem for the functions f(x) = x³ - 3x² + 2x in the interval [0, 2] is verified?

A
c = ± 1

B
c = 1 ± 1/ √3

C
c = ± 2

D
None of these

Solution